Ohm's Law and Circuits.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Physics 216\n",
    "#Plotting code to use the whole year!\n",
    "#Jaylene Naylor\n",
    "#September 2015, modified Sept 2017, August 2018\n",
    "#---------------------------------------\n",
    "#Import packages and libraries needed and give them shortcut names\n",
    "from __future__ import division\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#-------------------------------------------#\n",
    "#Data Section - Create Arrays for data. Perform necessary calculations\n",
    "#CHANGE THE VARIABLE NAMES and numbers to match your data\n",
    "xvariable_current = np.array([0.003,0.007,0.012,0.025,0.038,0.051,0.063,0.076,0.087,0.1,0.112,0.125]) #what are units?\n",
    "yvariable_voltage = np.array([0.26,0.54,0.972,2.008,3.056,4.009,5.030,6.008,6.95,7.95,8.95,9.97]) #what are units?\n",
    "\n",
    "\n",
    "#--------------------------------------------#\n",
    "#Create arrays for uncertainties\n",
    "#CHANGE THE VARIABLE NAME and numbers to match your data \n",
    "err_yvariable_R = np.array([1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687,1.5687])\n",
    "\n",
    "\n",
    "#--------------------------------------------#\n",
    "#Re-assign variables as x, y, dy so that the following code may remain generic\n",
    "\n",
    "x = xvariable_current   #this should be the array you want to plot on the x axis\n",
    "y = yvariable_voltage\n",
    "dy = err_yvariable_R  #this should be your error in y array\n",
    "\n",
    "#----------------------------------------------#\n",
    "#Don't need to change anything in this section!\n",
    " \n",
    "#Find the intercept and slope, b and m, from Python's polynomial fitting function\n",
    "b,m=np.polynomial.polynomial.polyfit(x,y,1,w=dy)\n",
    "\n",
    "#Write the equation for the best fit line based on the slope and intercept\n",
    "fit = b+m*x\n",
    "\n",
    "#Calculate the error in slope and intercept \n",
    "#def Delta(x, dy) is a function, and we will learn how to write our own at a later date. They are very useful!\n",
    "def Delta(x, dy):\n",
    "    D = (sum(1/dy**2))*(sum(x**2/dy**2))-(sum(x/dy**2))**2\n",
    "    return D\n",
    " \n",
    "D=Delta(x, dy)\n",
    " \n",
    "dm = np.sqrt(1/D*sum(1/dy**2)) #error in slope\n",
    "db = np.sqrt(1/D*sum(x**2/dy**2)) #error in intercept\n",
    "\n",
    "#Calculate the \"goodness of fit\" from the linear least squares fitting document\n",
    "def LLSFD2(x,y,dy):\n",
    "    N = sum(((y-b-m*x)/dy)**2)\n",
    "    return N\n",
    "                      \n",
    "N = LLSFD2(x,y,dy)\n",
    "\n",
    "#-----------------------------------------------------------------------#\n",
    "#Plot data on graph. Plot error bars and place values for slope, error in slope and goodness of fit on the plot using \"annotate\"\n",
    "plt.figure(figsize=(15,10))\n",
    " \n",
    "plt.plot(x, fit, color='green', linestyle='--')\n",
    "plt.scatter(x, y, color='blue', marker='o')\n",
    " \n",
    " \n",
    "#create labels  YOU NEED TO CHANGE THESE!!!\n",
    "plt.xlabel('Current (A)')\n",
    "plt.ylabel('Voltage (V)')\n",
    "plt.title('Resistance of a Resistor')\n",
    " \n",
    "plt.errorbar(x, y, yerr=dy, xerr=None, fmt=\"none\") #don't need to plot x error bars\n",
    " \n",
    "plt.annotate('Slope (V/A) = {value:.{digits}E}'.format(value=m, digits=2),\n",
    "             (0.05, 0.9), xycoords='axes fraction')\n",
    " \n",
    "plt.annotate('Error in Slope (V/A) = {value:.{digits}E}'.format(value=dm, digits=1),\n",
    "             (0.05, 0.85), xycoords='axes fraction')\n",
    " \n",
    "plt.annotate('Goodness of fit = {value:.{digits}E}'.format(value=N, digits=2),\n",
    "             (0.05, 0.80), xycoords='axes fraction')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The resistance of the unknown resistor is 79.6 +/- 1.57 Ohms. The accepted value for the resistance of the unknown resistor is 80.0 Ohms, so the calculated value agrees with the theoretical value.\n"
     ]
    }
   ],
   "source": [
    "print (\"The resistance of the unknown resistor is 79.6 +/- 1.57 Ohms. The accepted value for the resistance of the unknown resistor is 80.0 Ohms, so the calculated value agrees with the theoretical value.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}